Question: Rewrite as a simplified fraction. ${2.59\overline{4} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2594.4444...\\ 100x &= 259.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2335}$ ${x = \dfrac{2335}{900}} $ ${x = \dfrac{467}{180}} \text{or} {2 \dfrac{107}{180}}$